A systematic study of LTCs was initiated by Goldreich and Sudan in [1]}, and a sequence of works constructed both LTCs and PCPs with improved parameters [1]}, [3]}, [4]}, [5]}, [6]}, achieving constant locality and distance, but rate \(1/\operatorname{poly}\log n\) . Some experts believed that low rate is inherently needed and some attempts to prove upper bounds on the rate have been made [7]}, [8]}, [9]}, [10]}, although these lower bounds are in rather restrictive models.
